Abstract
In this paper we continue the program initiated in Part I, that is the study of entanglement measures in the sine-Gordon model. In both parts, we have focussed on one specific technique, that is the well-known connection between branch point twist field correlators and measures of entanglement in 1+1D integrable quantum field theory. Our papers apply this technique for the first time to a non-diagonal theory with an involved particle spectrum, the sine-Gordon model. In this Part II we focus on a different entanglement measure, the symmetry resolved entanglement, and develop its associated twist field description, exploiting the underlying U(1) symmetry of the theory. In this context, conventional branch point twist fields are no longer the fields required, but instead we must work with one of their composite generalisations, which can be understood as the field resulting from the fusion of a standard branch point twist field and the sine-Gordon exponential field associated with U(1) symmetry. The resulting composite twist field has correlators which as usual admit a form factor expansion. In this paper we write the associated form factor equations and solve them for various examples in the breather sector by using the method of angular quantisation. We show that, in the attractive regime, this is the sector which provides the leading contribution to the symmetry resolved entropies, both R\'enyi and von Neumann. We compute the latter in the limit of a large region size and show that they satisfy the property of equipartition, that is the leading contribution to the symmetry resolved entanglement is independent of the symmetry sector.
Highlights
It is natural to think of the composite branch point twist fields (CTF) we study in this paper as off-critical versions of their conformal counterparts (25)
In this paper we have extended our study of entanglement measures in the sine-Gordon model to the symmetry resolved entanglement entropy
It has been known for some time [63] that the symmetry resolved entropies can be expressed in terms of correlation functions of composite branch point twist fields
Summary
The quantum relativistic sine-Gordon (sG) model is one of the most studied low-dimensional quantum field theories. Via the bootstrap program all matrix elements are computable, the multi-point correlation functions at large distances are, usually dominated by the first few sets of form factors. This property has been often exploited in IQFTs and the use of BPTFs and their FFs have resulted in numerous interesting exact or very accurate predictions for the entanglement entropy under many different physical circumstances [47–61]. In 2D CFT, the symmetry resolved entropies have been obtained as multi-point correlations of the novel CTFs [63] These composite twist fields have been recently identified in some massive theories: free massive Dirac and complex boson QFT [74,75], the off-critical Ising and sinh-Gordon theories [76].
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